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The limit sets of subgroups of lattices in \(\mathrm {PSL}(2,\mathbb {R})^r\)

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Abstract

In this paper we give a description of the possible limit sets of finitely generated subgroups of irreducible lattices in \(\mathrm {PSL}(2,\mathbb {R})^r\).

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References

  1. Beardon, A.: The geometry of discrete groups, graduate texts in mathematics, vol. 91. Springer, New York (1995)

    Google Scholar 

  2. Benoist, Y.: Propriétés asymptotiques des groupes linéaires. Geom. Funct. Anal. 7, 1–47 (1997)

    Article  MathSciNet  Google Scholar 

  3. Borel, A.: Commensurability classes and volumes of hyperbolic 3-manifolds. Ann. Sc. Norm. Super. Pisa 8, 1–33 (1981)

    MathSciNet  MATH  Google Scholar 

  4. Cohen, P., Wolfart, J.: Modular embeddings for some non-arithmetic Fuchsian groups. Acta Arith. 61, 93–110 (1990)

    MathSciNet  MATH  Google Scholar 

  5. Eberlein, P.: Geometry of nonpositively curved manifolds, Chicago lectures in mathematics, vol. 1996. University of Chicago Press, Chicago (1996)

    MATH  Google Scholar 

  6. Geninska, S.: The limit set of subgroups of a class of arithmetic groups. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000014024, Dissertation, Karlsruhe (2009)

  7. Geninska, S.: The limit set of subgroups of arithmetic groups in \({\rm PSL}(2,\mathbb{C})^q\times {\rm PSL}(2,\mathbb{R})^r\). Groups Geom. Dyn. 8(4), 1047–1099 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Geninska, S.: Examples of infinite covolume subgroups of \({\rm PSL}(2,\mathbb{R})^r\) with big limit sets. Math. Zeit. 272, 389–404 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Leuzinger, E.: On the trigonometry of symmentric spaces. Comment. Math. Helvetici 67, 252–286 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  10. Link, G.: Limit sets of discrete groups acting on symmetric spaces. http://digbib.ubka.uni-karlsruhe.de/volltexte/7212002, Dissertation, Karlsruhe (2002)

  11. Link, G.: Geometry and dynamics of discrete isometry groups of higher rank symmetric spaces. Geom. Dedicata 122(1), 51–75 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Maclachlan, C., Reid, A.: The arithmetic of hyperbolic 3-manifolds, graduate texts in mathematics, vol. 219. Springer, Berlin (2003)

    Book  MATH  Google Scholar 

  13. Schaller, P.S., Wolfart, J.: Semi-arithmetic Fuchsian groups and modular embeddings. J. Lond. Math. Soc. (2) 61, 13–24 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tukia, P.: On isomorphisms of geometrically finite Möbius groups. Inst. Hautes Études Sci. Publ. Math. 61, 171–214 (1985)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Institut de Mathématiques de Toulouse, Université Toulouse 3, 118 route de Narbonne, 31062, Toulouse, France

    Slavyana Geninska

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  1. Slavyana Geninska
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Correspondence to Slavyana Geninska.

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Geninska, S. The limit sets of subgroups of lattices in \(\mathrm {PSL}(2,\mathbb {R})^r\) . Geom Dedicata 182, 81–94 (2016). https://doi.org/10.1007/s10711-015-0129-x

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  • DOI: https://doi.org/10.1007/s10711-015-0129-x

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